How can I tell if my mesh is detailed enough for boolean operations?
Sorry, but you can only get that knowledge by doing a series of misstakes. Subdivision is by no mean a silver bullet and neither is bevels. Subdivision is not a requirement for any model. It is a tool to handle a hi-poly surface with fewer controlling vertices. But it is hard to handle and you must take interest in how to make good topology for sub div.

If you do booleans the resulting topology will often be bad. It needs to be cleaned up. I would recommend you to analyse the result of each modifier and so you can learn how to control them.

It's not how much topology you have, more how it the edge flow works and that you have enough of it to support your shape.

I can recommend you to research how Arrimus 3D solves different problem, not always the same tools but more often then seldom a solution that works for blender.

https://www.youtube.com/channel/UCSLLdTBwLMfTKWS56tOiQpw